Theorems · Theorem · commutative algebra
expChar_of_injective_ringHom
∀ {R : Type u_1} {A : Type u_2} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring A] {f : R →+* A},
Function.Injective ⇑f → ∀ (q : ℕ) [hR : ExpChar R q], ExpChar A qIf a ring homomorphism R →+* A is injective then A has the same exponential characteristic
as R.
- Defined in
- Mathlib.Algebra.CharP.Algebra
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- Nat.Primeproof · cited by 2,059
- CharZeroproof · cited by 932
- NonAssocSemiringstatement and proof · cited by 805
- CharPproof · cited by 478
- ExpCharstatement and proof · cited by 276
- ExpChar.casesOnproof · cited by 21
- charP_of_injective_ringHomproof · cited by 5
- charZero_of_injective_ringHomproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- expChar_of_injective_algebraMapproof · cited by 8
- IsPurelyInseparable.injective_comp_algebraMapproof · cited by 3
- RingHom.expChar_iffproof · cited by 1
- minpoly.natSepDegree_eq_one_iff_eq_X_sub_C_powproof · cited by 1
- IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expCharproof · cited by 1
- Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparableproof · cited by 1
- ExpChar.of_injective_algebraMap'proof · cited by 0